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julsineya [31]
4 years ago
5

Please help me with this

Mathematics
1 answer:
hichkok12 [17]4 years ago
3 0
You need to find the area of the semi circle first which the formula is (pi)r^2/2. So 3.14159 ·(8)^2/2 is 101. Then find the area of the rectangle and subtract the area of the semi circle from the area of the rectangle! I hope this helps, I use ALEKS too. (I got 251 as a final answer, I'm p sure it's correct)
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Evaluate the Riemann sum for f(x) = 3 - 1/2 times x between 2 and 14 where the endpoints are included with six subintervals taki
Digiron [165]

Answer:

-6

Step-by-step explanation:

Given that :

we are to evaluate the Riemann sum for f(x) = 3 - \dfrac{1}{2}x from 2 ≤ x ≤ 14

where the endpoints are included with six subintervals, taking the sample points to be the left endpoints.

The Riemann sum can be computed as follows:

L_6 = \int ^{14}_{2}3- \dfrac{1}{2}x \dx = \lim_{n \to \infty} \sum \limits ^6 _{i=1} \ f (x_i -1) \Delta x

where:

\Delta x = \dfrac{b-a}{a}

a = 2

b =14

n = 6

∴

\Delta x = \dfrac{14-2}{6}

\Delta x = \dfrac{12}{6}

\Delta x =2

Hence;

x_0 = 2 \\ \\  x_1 = 2+2 =4\\ \\  x_2 = 2 + 2(2) \\ \\  x_i = 2 + 2i

Here, we are  using left end-points, then:

x_i-1 = 2+ 2(i-1)

Replacing it into Riemann equation;

L_6 =  \lim_{n \to \infty}  \sum \imits ^{6}_{i=1} \begin {pmatrix}3 - \dfrac{1}{2} \begin {pmatrix}  2+2 (i-1)  \end {pmatrix} \end {pmatrix}2

L_6 =  \lim_{n \to \infty}  \sum \imits ^{6}_{i=1} 6 - (2+2(i-1))

L_6 =  \lim_{n \to \infty}  \sum \imits ^{6}_{i=1} 6 - (2+2i-2)

L_6 =  \lim_{n \to \infty}  \sum \imits ^{6}_{i=1} 6 -2i

L_6 =  \lim_{n \to \infty}  \sum \imits ^{6}_{i=1} 6 -   \lim_{n \to \infty}  \sum \imits ^{6}_{i=1} 2i

L_6 =  \lim_{n \to \infty}  \sum \imits ^{6}_{i=1} 6 - 2  \lim_{n \to \infty}  \sum \imits ^{6}_{i=1} i

Estimating the integrals, we have :

= 6n - 2 ( \dfrac{n(n-1)}{2})

= 6n - n(n+1)

replacing thevalue of n = 6 (i.e the sub interval number), we have:

= 6(6) - 6(6+1)

= 36 - 36 -6

= -6

5 0
3 years ago
Change the decimal 0.0112 to a fraction
charle [14.2K]
112 over 10,000 because it is point zero-one hundred-twelve ten thousandths
4 0
3 years ago
PLEASE HELP ME!!!
Llana [10]

Answer:

Rent

Step-by-step explanation:

Yes

3 0
4 years ago
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Decrease seventy-two hundredths by two tenths. Write the equation used to solve this problem
sweet [91]
0.72
- .20
------------
0.52                                              (.20 is two tenths)
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MACRS depreciates automobiles in 6 years using these percents:
tia_tia [17]
Given that the book value of the automobile that was purchased is 30,000 and is to be depreciated for 3 years using MACRS method of depreciation the value of the automobile at the end of the year is 8,640 dollars.  This is computed by summing up the depreciation for the firswt 3 years which is equal to 71.2 per cent less 100 then it will be multiply to 30,000.
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